EP0862730A2 - Method for adaptive kalman filtering in dynamic systems - Google Patents
Method for adaptive kalman filtering in dynamic systemsInfo
- Publication number
- EP0862730A2 EP0862730A2 EP96938246A EP96938246A EP0862730A2 EP 0862730 A2 EP0862730 A2 EP 0862730A2 EP 96938246 A EP96938246 A EP 96938246A EP 96938246 A EP96938246 A EP 96938246A EP 0862730 A2 EP0862730 A2 EP 0862730A2
- Authority
- EP
- European Patent Office
- Prior art keywords
- values
- model
- matrix
- output signal
- calibration parameters
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01D—MEASURING NOT SPECIALLY ADAPTED FOR A SPECIFIC VARIABLE; ARRANGEMENTS FOR MEASURING TWO OR MORE VARIABLES NOT COVERED IN A SINGLE OTHER SUBCLASS; TARIFF METERING APPARATUS; MEASURING OR TESTING NOT OTHERWISE PROVIDED FOR
- G01D18/00—Testing or calibrating apparatus or arrangements provided for in groups G01D1/00 - G01D15/00
-
- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
- H03H21/00—Adaptive networks
- H03H21/0012—Digital adaptive filters
- H03H21/0025—Particular filtering methods
- H03H21/0029—Particular filtering methods based on statistics
- H03H21/003—KALMAN filters
Definitions
- the underlying Markov (finite memory) process is described by the equations from (1) to (3).
- Kalman gain matrix K is defined by ;
- c. typically represents calibration parameters at time t
- Augmented Model for a moving time volume (e.g. for "whitening” an observed “innovations” sequence of residuals e t for a moving sample of length L):
- the latter matrix equation has a "nested" Block- Angular structure.
- the first set of these parameters, c t can vary from one time to another.
- the second type, C t of these parameters have constant values (approximately at least) over long moving time windows of length L.
- the latter ones, C t make the Kalman filtering process an adaptive one.
- the solving of the latter parameters with the conventional Kalman recursions from (4) to (6) causes an observability problem as for computational reasons length L must be short. But with the FKF formulae of PCT/FI90/00122, the sample size can be so large that no initialization (or training) may be needed at all.
- the Augmented Model approach is superior to the use of the conventional Kalman recursions for a large vector of input data y. because the computation of the Kalman Gain matrix K requires the huge matrix inversion when Cov(s t ) is unknown. Both methods are algebraically and statistically equivalent but certainly not numerically.
- Matrix H is still the same design matrix as before that stemms from the partial derivatives of the physical dependencies between measurements y t and state parameters s. , please see Partitioning (11) on page 3 (the old block-diagonality assumption for matrices A and B is no longer valid). Matrix describes how the systematic errors of the measurements depend on the calibration or "calibration type" parameters, vector C t , that are constants in time or vary only slowly. The columns of matrices , , represent
- Matrix A t is still the same sta transition matrix that stemms from the partial derivatives of the physi l dependencies between states s and previous states s t-1 .
- r t is the column vector of all the mxm elements of matrix dA t .
- the matrix equation above has a "nested" Block- Angular structure.
- the first type, c t is imbedded in the data of each time step t.
- Two other types are represented by vector C t .
- the first set of these parameters, i.e. r t is used for correcting gross errors in the state transition matrices.
- the second set is used for the whitening and the partial ortogonalization of the errors of the measurements and the system (i.e. for block-diagonalization of covariance matrices).
- the last two sets of parameters have more or less constant values over the long moving time window and make the Kalman filtering process an adaptive one.
- Fig. 1 A supernavigator based on a notebook PC that performs the functions of a Kalman filtering logic unit (1) through exploiting the generalized Fast Kalman Filtering (FKF) method.
- the overall receiver concept comprises an integrated sensor, remote sensing, data processing and transmission system (3) of, say, a national atmospheric/oceanic service and, optionally, an off-the-shelf GPS receiver.
- the database unit (2) running on the notebook PC contains updated information on control (4) and performance aspects of the various subsystems as well as auxiliary information such as geographical maps.
- the logic unit (1) Based upon all these inputs, the logic unit (1) provides real-time 3-dimensional visualizations (5) on what is going on by using the FKF recursions for equation system (24) and on what will take place in the nearest future by using the predictions from equations (15). Dependable accuracy information is also provided when the well-known stability conditions of optimal Kalman filtering are be met by the observing system (3). These error variances and covariances are computed by using equations (15) and (20).
- the centralized data processing system (3) provides estimates of State Transition Matrix A for each time step t.
Abstract
Description
Claims
Priority Applications (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
SI9630624T SI0862730T1 (en) | 1995-11-15 | 1996-11-15 | Method for adaptive kalman filtering in dynamic systems |
Applications Claiming Priority (3)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
FI955489A FI955489A0 (en) | 1995-11-15 | 1995-11-15 | Foerfarande Foer adaptive Kalmanfiltrering in a dynamic system |
FI955489 | 1995-11-15 | ||
PCT/FI1996/000621 WO1997018442A2 (en) | 1995-11-15 | 1996-11-15 | Method for adaptive kalman filtering in dynamic systems |
Publications (2)
Publication Number | Publication Date |
---|---|
EP0862730A2 true EP0862730A2 (en) | 1998-09-09 |
EP0862730B1 EP0862730B1 (en) | 2003-05-14 |
Family
ID=8544385
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
EP96938246A Expired - Lifetime EP0862730B1 (en) | 1995-11-15 | 1996-11-15 | Method for adaptive kalman filtering in dynamic systems |
Country Status (25)
Country | Link |
---|---|
US (1) | US6202033B1 (en) |
EP (1) | EP0862730B1 (en) |
JP (1) | JPH11506204A (en) |
KR (1) | KR100392651B1 (en) |
CN (1) | CN1121093C (en) |
AU (1) | AU705080B2 (en) |
CA (1) | CA2236757C (en) |
CZ (1) | CZ293985B6 (en) |
DE (1) | DE69628186T2 (en) |
EA (1) | EA001188B1 (en) |
EE (1) | EE03534B1 (en) |
ES (1) | ES2198502T3 (en) |
FI (2) | FI955489A0 (en) |
GE (1) | GEP20022775B (en) |
IL (1) | IL124581A (en) |
IS (1) | IS4738A (en) |
MX (1) | MXPA98003895A (en) |
OA (1) | OA10768A (en) |
PL (1) | PL185573B1 (en) |
PT (1) | PT862730E (en) |
SI (1) | SI0862730T1 (en) |
SK (1) | SK284575B6 (en) |
TR (1) | TR199800947T2 (en) |
UA (1) | UA49862C2 (en) |
WO (1) | WO1997018442A2 (en) |
Families Citing this family (27)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US20020137696A1 (en) * | 1996-01-23 | 2002-09-26 | Robert Tam | Specific modulation of TH1/TH2 cytokine expression by ribavirin in activated T-lymphocytes |
FR2783940B1 (en) * | 1998-09-28 | 2000-12-01 | Schneider Electric Sa | METHOD OF ESTIMATING, USING AN EXTENDED KALMAN FILTER, A STATE VECTOR REPRESENTATIVE OF THE STATE OF A DYNAMIC SYSTEM |
WO2000075896A1 (en) | 1999-06-03 | 2000-12-14 | Boschung Mecatronic Ag | Method and warning device for generating glazed frost early warning signal for roads |
US6721770B1 (en) * | 1999-10-25 | 2004-04-13 | Honeywell Inc. | Recursive state estimation by matrix factorization |
US6564110B1 (en) * | 2000-06-07 | 2003-05-13 | Sumitomo Heavy Industries, Ltd. | Position controlling apparatus capable of reducing the effect of disturbance |
JP4031988B2 (en) * | 2001-01-30 | 2008-01-09 | トムソン ライセンシング | Apparatus for separating convolution mixed signals into multiple sound sources |
WO2002073351A2 (en) * | 2001-03-08 | 2002-09-19 | California Institute Of Technology | Real-time spatio-temporal coherence estimation for autonomous mode identification and invariance tracking |
US7050652B2 (en) | 2002-03-08 | 2006-05-23 | Anzus, Inc. | Methods and arrangements to enhance correlation |
US6803997B2 (en) * | 2002-03-08 | 2004-10-12 | Anzus, Inc. | Gridlocking and correlation methods and arrangements |
US6922493B2 (en) * | 2002-03-08 | 2005-07-26 | Anzus, Inc. | Methods and arrangements to enhance gridlocking |
US6909808B2 (en) * | 2002-03-08 | 2005-06-21 | Anzus, Inc. | Image compression to enhance optical correlation |
GB0207431D0 (en) * | 2002-03-28 | 2002-05-08 | Qinetiq Ltd | Signal analysis system |
JP3966139B2 (en) * | 2002-09-27 | 2007-08-29 | 株式会社日立製作所 | Meteorological quantity estimation method |
US7276877B2 (en) * | 2003-07-10 | 2007-10-02 | Honeywell International Inc. | Sensorless control method and apparatus for a motor drive system |
US6961677B1 (en) * | 2003-08-25 | 2005-11-01 | Itt Manufacturing Enterprises, Inc. | Method and apparatus for categorizing unexplained residuals |
JP5020807B2 (en) * | 2004-03-23 | 2012-09-05 | ザ リージェンツ オブ ザ ユニバーシティ オブ カリフォルニア | Apparatus and method for enhancing the reliability of sensor data collected on a network |
CN101048714B (en) * | 2004-08-27 | 2010-05-12 | 西门子共同研究公司 | System, device, and methods for updating system-monitoring models |
CN100389302C (en) * | 2004-11-12 | 2008-05-21 | 厦门信源交通器材有限公司 | Method for predicting engine crankshaft corner and speed revolution value with kalman filter |
WO2007096466A1 (en) * | 2006-02-27 | 2007-08-30 | Antti Aarne Llmari Lange | A method for calibrating teh carrier-phases of radio signals from satellites and other transmitters by using fast kalman filtering |
CN100483276C (en) * | 2006-06-02 | 2009-04-29 | 中国科学院自动化研究所 | Self-adapting state feedback forecasting control method based on noise computing |
US7605747B1 (en) * | 2006-08-14 | 2009-10-20 | Lockheed Martin Corporation | Method for compensating for the positional errors of a sensor |
US8600660B2 (en) * | 2006-09-29 | 2013-12-03 | Honeywell International Inc. | Multipath modeling for deep integration |
US20090299929A1 (en) * | 2008-05-30 | 2009-12-03 | Robert Kozma | Methods of improved learning in simultaneous recurrent neural networks |
CN102890743B (en) * | 2011-07-19 | 2015-08-05 | 北京理工大学 | Planetary scale enters lander drop point analysis on Uncertainty method |
JP6117349B2 (en) * | 2012-06-19 | 2017-04-19 | ゲーコーエヌ エアロスペース スウェーデン アーベー | Simple calculation model generation method and component consumption life prediction method |
US9825641B1 (en) * | 2014-09-12 | 2017-11-21 | The United States Of America As Represented By The Administrator Of The National Aeronautics And Space Administration | Reconfigurable sensor monitoring system |
RU2755499C1 (en) * | 2021-01-28 | 2021-09-16 | Ордена Трудового Красного Знамени федеральное государственное бюджетное образовательное учреждение высшего образования «Московский технический университет связи и информатики» (МТУСИ). | Adaptive filtering method |
Family Cites Families (6)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
JPS57116410A (en) * | 1981-01-13 | 1982-07-20 | Kokusai Denshin Denwa Co Ltd <Kdd> | Karman type equalizer |
US4760596A (en) * | 1986-02-25 | 1988-07-26 | Gte Laboratories Incorporated | Adaptive echo cancellation and equalization system signal processor and method therefor |
FI896219A0 (en) * | 1989-04-28 | 1989-12-22 | Antti Aarne Ilmari Lange | ANALYZING AND FOUNDATION CALIBRATION AV DETEKTORSYSTEM. |
FI922031A0 (en) * | 1991-10-23 | 1992-05-05 | Antti Aarne Ilmari Lange | FOERFARANDE FOER KALMAN-FILTER I STORA SYSTEM. |
CA2106368A1 (en) * | 1992-01-16 | 1993-07-17 | Theodore E. Maione | Methods and compositions for treatment of angiogenic disease |
US5991525A (en) * | 1997-08-22 | 1999-11-23 | Voyan Technology | Method for real-time nonlinear system state estimation and control |
-
1995
- 1995-11-15 FI FI955489A patent/FI955489A0/en not_active Application Discontinuation
-
1996
- 1996-11-15 PL PL96327042A patent/PL185573B1/en not_active IP Right Cessation
- 1996-11-15 SK SK1137-98A patent/SK284575B6/en not_active IP Right Cessation
- 1996-11-15 WO PCT/FI1996/000621 patent/WO1997018442A2/en active IP Right Grant
- 1996-11-15 PT PT96938246T patent/PT862730E/en unknown
- 1996-11-15 MX MXPA98003895A patent/MXPA98003895A/en active IP Right Grant
- 1996-11-15 GE GEAP1996004344 patent/GEP20022775B/en unknown
- 1996-11-15 US US09/074,933 patent/US6202033B1/en not_active Expired - Lifetime
- 1996-11-15 CA CA002236757A patent/CA2236757C/en not_active Expired - Fee Related
- 1996-11-15 AU AU75742/96A patent/AU705080B2/en not_active Ceased
- 1996-11-15 DE DE69628186T patent/DE69628186T2/en not_active Expired - Fee Related
- 1996-11-15 EP EP96938246A patent/EP0862730B1/en not_active Expired - Lifetime
- 1996-11-15 KR KR10-1998-0703684A patent/KR100392651B1/en not_active IP Right Cessation
- 1996-11-15 TR TR1998/00947T patent/TR199800947T2/en unknown
- 1996-11-15 ES ES96938246T patent/ES2198502T3/en not_active Expired - Lifetime
- 1996-11-15 IL IL12458196A patent/IL124581A/en not_active IP Right Cessation
- 1996-11-15 JP JP9518609A patent/JPH11506204A/en active Pending
- 1996-11-15 UA UA98063074A patent/UA49862C2/en unknown
- 1996-11-15 EE EE9800143A patent/EE03534B1/en not_active IP Right Cessation
- 1996-11-15 SI SI9630624T patent/SI0862730T1/en unknown
- 1996-11-15 EA EA199800444A patent/EA001188B1/en not_active IP Right Cessation
- 1996-11-15 CZ CZ19982554A patent/CZ293985B6/en not_active IP Right Cessation
- 1996-11-15 CN CN96198347A patent/CN1121093C/en not_active Expired - Fee Related
-
1998
- 1998-05-12 IS IS4738A patent/IS4738A/en unknown
- 1998-05-15 OA OA9800055A patent/OA10768A/en unknown
- 1998-05-15 FI FI981095A patent/FI114412B/en not_active IP Right Cessation
Non-Patent Citations (1)
Title |
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See references of WO9718442A2 * |
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